The influence of magnetic field intensity on creep deformation

In this subsection and the two following ones the results regarding the study of the influence of the magnetic field on the creep deformation process of 2605SA1 metallic glass are presented. Since the magnetic field is a vectorial quantity, and so is the stress, not only it intensity should be considered but also it orientation with respect to the mechanical stress. Taking that into account, the study of the magnetic field effect is divided in three subsections, which focuses on the influence of it intensity, and orientation. The study of the orientation is as well divided into two independent parts which study the influence of the angle 𝜃 within a plane perpendicular to the stress and the angle 𝜙 with respect to the stress.

The experiments shown in the current subsection focus on the study of the influence of the intensity of the magnetic field. Since it turned out that the influence of the magnetic field depends itself on the mechanical load, all the experiments were performed for two different tensile stresses, 𝜎 = 15 and 𝜎 = 25 MPa. Figure 5.21 (a) shows a set of creep experiments performed at ^T

Tg= 0.8, 𝜎 = 15 and several intensities of magnetic field applied along the width direction of the ribbon (𝜃 = 0, 𝜙 = 0). As shown in Figure 5.12 the sample magnetization decreases with temperature.

Therefore, the temperature of the experiments was chosen to be the lowest at which the sample deforms sufficiently in order to be able to perform a waiting times analysis.

Figure 5.21(b) shows the waiting time distribution calculated for the experiments shown in Figure 5.21(a). A power law regime can be appreciated in the double logarithmic plot, as well as an initial higher slope, which suggest a crossover in the waiting time distribution. The cut-off is shifted to shorter waiting times when the magnetic field was applied.

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Figure 5.21 (a) Creep measurements of 2605SA1 performed at _𝑇^𝑇

𝑔= 0.8, 𝜎 = 15 for different intensities of magnetic field oriented along the width direction (𝜃 = 0, 𝜙 = 0).

(b) Double logarithmic representation of the waiting time distribution calculated from the creep measurements shown in (a)

Figure 5.22 shows the waiting time distribution splitting the data between before and after the crossover time 𝑡_{𝑐𝑟𝑜𝑠𝑠}. It can be seen in Figure 5.22 (a)-(e) that there is a significant change of slope at 𝑡_{𝑐𝑟𝑜𝑠𝑠}, but the power law shape is well preserved in each of the cases. Figure 5.22 (f) shows the fit of the experimental power laws and it demonstrates that, except the measurement at |𝐻⃗⃗⃗| = 640 Oe, the values of the experimental exponents before (𝜏₁) and after (𝜏₂) the crossover are contained in the range 𝜏₁ = −1.5 ± 0.1 and 𝜏₂= −0.8 ± 0.1. The experiment corresponding to

|𝐻⃗⃗⃗| = 640 Oe presents a lower slope of 𝜏₂~ − 0.5 in the second regime.

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Figure 5.22 Waiting time distributions before and after the crossover time, for the creep measurements of 2605SA1 ribbons at temperature _𝑇^𝑇

𝑔= 0.8, 𝜎 = 15 MPa and under several intensities of magnetic field along the width direction (𝜃 = 0, 𝜙 = 0). (a) |𝐻⃗⃗⃗| = 0 Oe. (b) |𝐻⃗⃗⃗| = 150 Oe. (c) |𝐻⃗⃗⃗| = 340 Oe. (d) |𝐻⃗⃗⃗| = 500 Oe. (e) |𝐻⃗⃗⃗| = 640 Oe. (f) Fit of the power law exponents before and after the crossover calculated from the curves (a)-(e), the shaded areas represent the intervals 𝜏₁= −1.5 ± 0.1 and 𝜏₂= −0.8 ± 0.1.

The three figures of merit, 𝑡_{𝑐𝑟𝑜𝑠𝑠}, 𝑡_𝜀̇ and 𝑊, are shown in Figure 5.23. All of three magnitudes present a maximum which is located in the range 150-500 Oe, which matches the value of the anisotropy field along the width orientation H_A^W= 300 ± 20 Oe shown in figure 5.12. All the values of applied field are higher than the coercive field which is estimated to be H_c ≈ 10 Oe. Such maximum of the figures of merit can be interpreted in terms of the orientation of domain walls and and will be discussed in next section.

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Figure 5.23 (a) Dependence of 𝑡_{𝑐𝑟𝑜𝑠𝑠} and 𝑡_𝜀̇ with the magnetic field intensity applied along the width direction (𝜃 = 0, 𝜙 = 0), calculated from creep measurements on 2605SA1 ribbons for a fixed temperature _𝑇^𝑇

𝑔= 0.8 and several stresses. (b) 𝑊as a function of magnetic field intensity, applied along the width direction (𝜃 = 0, 𝜙 = 0), calculated from creep measurements on 2605SA1 ribbons for a fixed temperature _𝑇^𝑇

𝑔= 0.8 and stress 𝜎 = 15 MPa.

As was previously stated, the influence of the magnetic field intensity is expected to be stress dependent. All the measurements shown in this subsection, were repeated for a higher value of mechanical stress 𝜎 = 25 MPa. Figure 5.24 (a) displays the creep curves measured at _T^T

g= 0.8, 𝜎 = 25 and several intensities of magnetic field applied along the width direction of the ribbon (𝜃 = 0, 𝜙 = 0). Figure 5.24(b) shows the waiting time distribution calculated from such creep measurements. A power law regime can be clearly seen, as well as an initial higher slope, which suggest a crossover in the waiting times statistics.

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Figure 5.24 (a) Creep measurements of 2605SA1 perfermed at _𝑇^𝑇

𝑔= 0.8, 𝜎 = 25 for different intensities of magnetic field oriented along the width direction (𝜃 = 0, 𝜙 = 0). (b) Double logarithmic representation of the waiting time distribution calculated from the creep measurements shown in (a)

Figure 5.25 shows the waiting time distribution splitting the data between before and after the crossover time 𝑡_{𝑐𝑟𝑜𝑠𝑠}. It can be seen in Figure 5.25(a)-(e) that there is a significant change of slope at 𝑡_{𝑐𝑟𝑜𝑠𝑠}, but the power law shape is well preserved in each of the cases. Figure 5.22(f) shows the fit of the experimental power laws and it can be seen that the experimental exponents before (𝜏₁) and after (𝜏₂) the crossover oscillate around the values 𝜏₁= −1.5 and 𝜏₂ = −0.8. However, in this set of experiments some of the deviations are larger than ±0.1. particularly, the experiment performed at H=340 Oe shows a dip and peak of the first and second exponents 𝜏₁, 𝜏₂ respectively.

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Figure 5.25 Waiting time distributions before and after the crossover time, for the creep measurements of 2605SA1 ribbons at temperature _𝑇^𝑇

𝑔= 0.8, 𝜎 = 25 MPa and under several intensities of magnetic field along the width orientation (𝜃 = 0, 𝜙 = 0). (a) |𝐻⃗⃗⃗| = 0 Oe. (b) |𝐻⃗⃗⃗| = 150 Oe. (c) |𝐻⃗⃗⃗| = 340 Oe. (d) |𝐻⃗⃗⃗| = 500 Oe. (e) |𝐻⃗⃗⃗| = 640 Oe. (f) Fit of the power law exponents before and after the crossover calculated from the curves (a)-(e), the dashed areas represent the intervals 𝜏₁= −1.5 ± 0.1 and 𝜏₂= −0.8 ± 0.1.

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Last, the three figures of merit, 𝑡_{𝑐𝑟𝑜𝑠𝑠}, 𝑡_𝜀̇ and 𝑊, are shown in Figure 5.26. In contrast with the creep measurements at 𝜎 = 15 MPa, these magnitudes do not show a maximum. Instead, they increase almost monotonically with increasing magnetic field. This change in behavior in comparison with the measurements at 𝜎 = 15 MPa will be analyzed and discussed in Section 6, and will be interpreted in terms of the anisotropy field 𝐻_𝐴(𝜎), which is stress-dependent.

Figure 5.26 (a) Dependence of 𝑡_{𝑐𝑟𝑜𝑠𝑠} and 𝑡_𝜀̇ with the magnetic field intensity applied along the width direction (𝜃 = 0, 𝜙 = 0) calculated from creep measurements on 2605SA1 for a fixed temperature _𝑇^𝑇

𝑔= 0.8 and stress 𝜎 = 25 MPa. (b) 𝑊 as a function of magnetic field intensity applied along the width direction (𝜃 = 0, 𝜙 = 0) calculated from creep measurements on 2605SA1 for a fixed temperature _𝑇^𝑇

𝑔= 0.8 and stress 𝜎 = 25 MPa.

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